Interval Analysis for Decision Aiding

Abstract

The interval analysis for decision aiding based on the possibility theory is introduced. The interval analysis provides a new paradigm of data analysis which is based on the idea that the variability of the data is not always caused by the error but by the intrinsic variety of the systems outputs. From this idea, several methods for data analysis have been proposed and obtained results in a different point of view from the conventional analysis. First, the interval regression analysis is briefly introduced dividing into two cases: the case of crisp data and the case of interval data. Then the application to Analytic Hierarchy Process (AHP) called Interval AHP is described. This method can be seen as the AHP counterpart of the interval regression analysis for crisp data. A proper method for the comparison between alternatives is proposed. The obtained dominance relation between alternatives is not always a total order but a preorder. Finally, the extension of Interval AHP to Group Interval AHP is described. This method can be seen as the AHP counterpart of the interval regression analysis for interval data. We describe three models of Group Interval AHP, i.e., perfect incorporation model, partial incorporation model and seeking common ground model. In each model, we obtain the dominance relations between alternatives which are usually preorders but have different meanings. The relationship among the three models is described.